1. Assessment of the Walleye Pollock Stock in the Gulf of Alaska

Executive Summary

Testing tables ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ??

Testing figures Figures 1.2

Summary of Changes in Assessment Inputs

Changes to input data

1. Fishery: 2021 total catch and catch at age.
2. Shelikof Strait acoustic survey: 2022 biomass index and age composition.
3. NMFS bottom trawl survey: 2021 age compositions
4. Summer acoustic survey: 2021 age compositions
5. ADF&G crab/groundfish trawl survey: 2022 biomass index

Changes in assessment methodology

Two minor changes were made to the model. First, a penalty of 1.3 was added to recruitment deviations in all years. Previously the penalty of 1.0 was applied only to early and late deviations. Second, selectivity of the summer acoustic survey was estimated. Previously this was assumed 1.0 for all ages. Together these changes constitute model 19.1a.

Summary of Results

The base model projection of female spawning biomass in 2022 is 204,554 t, which is 43.6149254 % of unfished spawning biomass (based on average post-1977 recruitment) and above B40% (188,000 t), thereby placing GOA pollock in sub-tier “a” of Tier 3. New surveys in 2022 include the winter Shelikof Strait acoustic survey and the ADF&G bottom trawl survey. Similar to 2021 these showed similar trends, unlike previous years when the surveys showed strongly contrasting trends. The risk matrix table recommended by the SSC was used to determine whether to recommend an ABC lower than the maximum permissible. The table is applied by evaluating the severity of four types of considerations that could be used to support a scientific recommendation to reduce the ABC from the maximum permissible. Although we identified some aspects of the stock that merit close tracking, there were no elevated concerns about stock assessment, population dynamics, environment/ecosystem, or fisheries performance categories. We therefore recommend no reduction from maximum permissible ABC.

The authors’ 2023 ABC recommendation for pollock in the Gulf of Alaska west of 140° W lon. (W/C/WYK regions) is 148,937 t, which is an increase of 11.9145483 from the 2021 ABC. The author’s recommended 2024 ABC is 161,080 t. The OFL in 2023 is 173,470 t, and the OFL in 2024 if the ABC is taken in 2023 is 186,101 t. These calculations are based on a projected 2022 catch of 129,754 t. The estimated scale of the stock increased compared to previous years, driven both by new data and model changes.

For pollock in southeast Alaska (Southeast Outside region, east of 140° W lon.), the ABC recommendation for both 2023 and 2024 is 11,363 t (see Appendix 1B) and the OFL recommendation for both 2023 and 2024 is 15,150 t. These recommendations are based on a Tier 5 assessment using the projected biomass in 2022 and 2023 from a random effects model fit to the 1990-2021 bottom trawl survey biomass estimates of the assessment area.

Status Summary for Gulf of Alaska Pollock in W/C/WYK Areas

## Status Summary for Gulf of Alaska Pollock in the Southeast Outside Area

Responses to SSC and Plan Team Comments on Assessments in General

None this year.

Responses to SSC and Plan Team Comments Specific to this Assessment

Detailed analyses to SSC and Plan Team comments were presented at the September PT meeting, including a publically available document to which the interested reader is referred (link to pdf)

Summaries of responses are provided here.

In December 2021 the SSC noted “… that recruitment deviations in the GOA pollock assessment are unconstrained except for the terminal two years, and suggests that exploring a moderate constraint on recruitment deviations in all years, as is commonly applied in other assessments, may be warranted. At a minimum, this would allow an assessment of the sensitivity of results to only constraining the last two years.”

Previous model versions applied a penalty of \(\sigma_R=1\) to the first eight and last two cohorts, with all other deviations being freely estimated. Historically this setup had no estimation issues, but there are some advantages to a consistent approach and so this approach was adopted. A value of \(\sigma_R=1.3\) was adopted, based on an estimate from a state-space version of the assessment, and applied to all deviates.

The GOA Plan Team in its November 2019 minutes recommended the author examine fishery selectivity, as persistent patterns in the catch-at-age residuals may represent artifacts of the selectivity functional form used.

Analyses performed in 2021 were extended to include an offset for age-4 fish, which did improve the fits to the data but had minimal impact on the assessment outputs. This showed that the persistent residuals were not adversely affecting management estimates, and that it is unlikely any parametric form would alleviate this issue. Consequently, no changes were made to this years model, but future analyses using non-parametric selectivity would be warranted.

Persistent patterns in Pearson residuals for older fish were also deemed not a concern at the moment. This is because a new way of calculating residuals using a “one step ahead” approach to account for correlations in the multinomial distribution (Trijoulet et al. 2023), which did not show the same pattern, implying it was a consequence of the inadequateness of Pearson residuals and not a real misspecification of selectivity.

In December 2021 the “SSC suggests simplifying the computations in the Appendix to reflect the new season structure to the extent possible, without changing the underlying methodology. For example, it appears that seasons B1 & B2 (formerly C & D) could be combined as they use the same apportionment scheme.”

The apportionment table will be simplified where possible to reflect the new seasonal structure. Note that this new structure was not supposed to change apportionment, and that motivates the current table which calculates by the previous four seasons and then sums them together into the new seasons.

…the SSC encourages the authors and GOA GPT to re-evaluate whether assessing Southeast Alaska walleye pollock as a separate stock is justified or whether the available data support a single, gulf-wide stock assessment. This evaluation may also benefit from considering recent studies on the genetic structure of walleye pollock across Alaska and the North Pacific

A genetic analysis using low-coverage whole genome sequencing was recently conducted, on which analysis is ongoing. This analysis included 617 walleye pollock from Japan, Bering Sea, Chukchi Sea, Aleutian Islands, Alaska Peninsula, and Gulf of Alaska. Results suggests there is temporally stable stock structure with a latitudinal gradient, i.e., Bering Sea pollock are distinguishable from those in the Gulf of Alaska and Aleutian Islands (I. Spies, personal communication, 2021). Samples from the eastern Gulf of Alaska are currently undergoing sequencing to determine whether eastern Gulf of Alaska pollock are genetically distinct from those in the western Gulf of Alaska. An evaluation of stock structure for Gulf of Alaska pollock following the template developed by NPFMC stock structure working group was provided as an appendix to the 2012 assessment (dorn2012?). Available information supported the current approach of assessing and managing pollock in the eastern portion of the Gulf of Alaska (Southeast Outside) separately from pollock in the central and western portions of the Gulf of Alaska (Central/Western/West Yakutat).

In December 2021 the SSC highlighted the need to examine how catchability for the winter Shelikof acoustic survey.

The SSC supports future research to identify the optimal level of constraint on among-year variation in Shelikof Survey catchability (q), including the potential to estimate the process error variance internally within the assessment model.

The SSC reiterates its recommendation from December 2020 to explore the use of covariates related to the timing of the survey to inform survey catchability in the Shelikof Strait survey. For example, the difference in timing between peak spawning and mean survey date or, alternatively, the proportion of mature fish in the survey, are likely to inform time-varying catchability in the survey.

Currently the winter Shelikof acoustic survey catchability is modeled as a random walk with assumed process error. The original logic was that some of the stock spawned outside of Shelikof Strait and thus were unavailable to the survey. Fish tended to spawn in other areas with some consistency, so a random walk on catchability was implemented to account for variation in spatial availability. Several overlapping efforts were done to explore alternative catchability structures. None of these are proposed for 2022, but were presented for Plan Team feedback in September 2022 and remains ongoing collaborative research for this stock. In particular a WHAM version of the GOA pollock assessment was used to explore estimating the constrait (process error), and to quantify the amount by which timing covariates can reduce that, in effect parsing spatial and temporal availability.

Introduction

Biology and Distribution

Walleye pollock (Gadus chalcogrammus; hereafter referred to as pollock) is a semi-pelagic schooling fish widely distributed in the North Pacific Ocean. Pollock in the central and western Gulf of Alaska (GOA) are managed as a single stock independently of pollock in the Bering Sea and Aleutian Islands. The separation of pollock in Alaskan waters into eastern Bering Sea and Gulf of Alaska stocks is supported by analysis of larval drift patterns from spawning locations (Bailey et al. 1997), genetic studies of allozyme frequencies (grant1980?), mtDNA variability (Mulligan et al. 1992), and microsatellite allele variability (baily1997a?).

Stock Structure

The results of studies of stock structure within the Gulf of Alaska are equivocal. There is evidence from allozyme frequency and mtDNA that spawning populations in the northern part of the Gulf of Alaska (Prince William Sound and Middleton Island) may be genetically distinct from the Shelikof Strait spawning population (olsen2002?). However, significant variation in allozyme frequency was found between Prince William Sound samples in 1997 and 1998, indicating a lack of stability in genetic structure for this spawning population. (olsen2002?) suggest that interannual genetic variation may be due to variable reproductive success, adult philopatry, source-sink population structure, or utilization of the same spawning areas by genetically distinct stocks with different spawning timing. There are important recent preliminary results from a genetic analysis of 617 walleye pollock from Japan, Bering Sea, Chukchi Sea, Aleutian Islands, Alaska Peninsula, and Gulf of Alaska using low-coverage whole genome sequencing. Results suggests there is a temporally stable stock structure with a latitudinal gradient, i.e., Bering Sea pollock are distinguishable from those in the Gulf of Alaska and Aleutian Islands (I. Spies, personal communication, 2021). An evaluation of stock structure for Gulf of Alaska pollock following the template developed by NPFMC stock structure working group was provided as an appendix to the 2012 assessment (dorn2012?). Available information supported the current approach of assessing and managing pollock in the eastern portion of the Gulf of Alaska (Southeast Outside) separately from pollock in the central and western portions of the Gulf of Alaska (Central/Western/West Yakutat). The main part of this assessment deals only with the C/W/WYK stock, while results for a tier 5 assessment for southeast outside pollock are reported in Appendix 1B.

Fishery

The commercial fishery for walleye pollock in the Gulf of Alaska started as a foreign fishery in the early 1970s (Megrey 1989). Catches increased rapidly during the late 1970s and early 1980s (Table 1.??). A large spawning aggregation was discovered in Shelikof Strait in 1981, and a fishery developed for which pollock roe was an important product. The domestic fishery for pollock developed rapidly in the Gulf of Alaska with only a short period of joint venture operations in the mid-1980s. The fishery was fully domestic by 1988.

Description of the Directed Fishery

Catch Patterns

The pollock target fishery in the Gulf of Alaska is entirely shore-based with approximately 96% of the catch taken with pelagic trawls. During winter, fishing effort targets pre-spawning aggregations in Shelikof Strait and near the Shumagin Islands (Fig. 1.2). Fishing in summer is less predictable, but typically occurs in deep-water troughs on the east side of Kodiak Island and along the Alaska Peninsula.

Bycatch and Discards

Incidental catch in the Gulf of Alaska directed pollock fishery is low. For tows classified as pollock targets in the Gulf of Alaska between 2016 and 2020, on average about 96% of the catch by weight of FMP species consisted of pollock (Table 1.2). Nominal pollock targets are defined by the dominance of pollock in the catch, and may include tows where other species were targeted, but pollock were caught instead. The most common managed species in the incidental catch are arrowtooth flounder, Pacific ocean perch, Pacific cod, sablefish, shallow-water flatfish, and flathead sole (Table 1.2). Sablefish incidental catch has trended upwards since 2018, perhaps reflecting both the recent increase in sablefish abundance and a wider spatial distribution. The most common recent non-target species are grenadiers, squid, capelin, jellyfish and miscellaneous fish (Table 1.2). Bycatch estimates for prohibited species over the period 2016-2020 are given in Table 1.3. Chinook salmon are the most important prohibited species caught as bycatch in the pollock fishery. A sharp spike in Chinook salmon bycatch in 2010 led the Council to adopt management measures to reduce Chinook salmon bycatch, including a cap of 25,000 Chinook salmon bycatch in the directed pollock fishery. Estimated Chinook salmon bycatch since 2010 has been less than the peak in 2010, with increases in 2016, 2017, and 2019, and reduced to 10,867 in 2020.

Management Measures

Since 1992, the Gulf of Alaska pollock Total Allowable Catch (TAC) has been apportioned spatially and temporally to reduce potential impacts on Steller sea lions. The details of the apportionment scheme have evolved over time, but the general objective is to allocate the TAC to management areas based on the distribution of surveyed biomass, and to establish three or four seasons between mid-January and fall during which some fraction of the TAC can be taken. The Steller Sea Lion Protection Measures implemented in 2001 established four seasons in the Central and Western GOA beginning January 20, March 10, August 25, and October 1, with 25% of the total TAC allocated to each season. Allocations to management areas 610, 620 and 630 are based on the seasonal biomass distribution as estimated by groundfish surveys. In addition, a harvest control rule was implemented that requires suspension of directed pollock fishing when spawning biomass declines below 20% of the reference unfished level.

Recently NMFS approved the final rule for Amendment 109 to GOA Fishery Management Plan developed by the North Pacific Fisheries Management Council. Amendment 109 combines pollock fishery A and B seasons into a single season (redesignated as the A season), and the C and D seasons into a single season (redesignated as the B season), and changes the annual start date of the redesignated pollock B season from August 25 to September 1. These changes will be implemented beginning in 2021 and affect the seasonal allocation only in the Central and Western GOA.

Data

The data used in the assessment model consist of estimates of annual catch in tons, fishery age composition, NMFS summer bottom trawl survey estimates of biomass and age and length composition, acoustic survey estimates of biomass and age composition in Shelikof Strait, summer acoustic survey estimates of biomass and age and length composition, and ADF&G bottom trawl survey estimates of biomass and age composition. Binned length composition data are used in the model only when age composition estimates are unavailable, such as the most recent surveys. The following table specifies the data that were used in the GOA pollock assessment:

Fishery

Catch

Total catch estimates were obtained from INPFC and ADF&G publications, and databases maintained at the Alaska Fisheries Science Center and the Alaska Regional Office. Foreign catches for 1963-1970 are reported in Forrester et al. (1978). During this period only Japanese vessels reported catch of pollock in the GOA, though there may have been some catches by Soviet Union vessels. Foreign catches 1971-1976 are reported by Forrester et al. (1983). During this period there are reported pollock catches for Japanese, Soviet Union, Polish, and South Korean vessels in the Gulf of Alaska. Foreign and joint venture catches for 1977-1988 are blend estimates from the NORPAC database maintained by the Alaska Fisheries Science Center. Domestic catches for 1970-1980 are reported in Rigby (1984). Domestic catches for 1981-1990 were obtained from PacFIN (Brad Stenberg, pers. comm. Feb 7, 2014). A discard ratio (discard/retained) of 13.5% was assumed for all domestic catches prior to 1991 based on the 1991-1992 average discard ratio. Estimated catch for 1991-2020 was obtained from the Catch Accounting System database maintained by the Alaska Regional Office. These estimates are derived from shoreside electronic logbooks and observer estimates of at-sea discards (Table 1.4). Catches include the state-managed pollock fishery in Prince William Sound (PWS). Since 1996, the pollock Guideline Harvest Level (GHL) of 2.5% for the PWS fishery has been deducted from the total Acceptable Biological Catch (ABC) by the NPFMC Gulf of Alaska Plan Team for management purposes (see SAFE introduction for further information). Non-commercial catches are reported in Appendix 1E.

Age and Size Composition

Catch at age was re-estimated in the 2014 assessment for 1975-1999 from primary databases maintained at AFSC. A simple non-stratified estimator was used, which consisted of compiling a single age-length key for use in every year and the applying the annual length composition to that key. Use of an age-length key was considered necessary because observers used length-stratified sampling designs to collect otoliths prior to 1999 (Barbeaux et al. 2005). Estimates were made separately for the foreign/JV and domestic fisheries in 1987 when both fisheries were sampled. There were no major discrepancies between the re-estimated age composition and estimates that have built up gradually from assessment to assessment.

Estimates of fishery age composition from 2000 onwards were derived from at-sea and port sampling of the pollock catch for length and ageing structures (otoliths). The length composition and ageing data were obtained from the NORPAC database maintained at AFSC. Catch age composition was estimated using methods described by Kimura and Chikuni (1989). Age samples were used to construct age-length keys by sex and stratum. These keys were applied to sex and stratum specific length frequency data to estimate age composition, which were then weighted by the catch in numbers in each stratum to obtain an overall age composition. A background age-length key is used fill the gaps in age-length keys by sex and stratum. Sampling levels by stratum for 2000-2015 are documented in the assessments available online at http://www.afsc.noaa.gov/REFM/stocks/Historic_Assess.htm. Age and length samples from the 2020 fishery were stratified by half-year seasons and statistical area as follows:

table TODO

The estimated age composition in 2020 in all areas and all seasons was notable because it was not dominated by age-8 fish (2012 year class) for the first time in many years (Fig. 1.2). Instead, the age-3 fish had the largest percentage with 38% while the age-8 fish only accounting for 29%. Younger fish are likely to become increasingly prominent in the catch-at-age as the 2012 year class begins age out of the population. Fishery catch at age in 1975-2020 is presented in Table 1.5 (See also Fig. 1.3). Sample sizes for ages and lengths are given in Table 1.6.

Gulf of Alaska Bottom Trawl Survey

Trawl surveys have been conducted by Alaska Fisheries Science Center (AFSC) beginning in 1984 to assess the abundance of groundfish in the Gulf of Alaska (Table 1.7). Starting in 2001, the survey frequency was increased from once every three years to once every two years. The survey uses a stratified random design, with 49 strata based on depth, habitat, and statistical area (von Szalay et al. 2010). Area-swept biomass estimates are obtained using mean CPUE (standardized for trawling distance and mean net width) and stratum area. The survey is conducted from chartered commercial bottom trawlers using standardized poly-Nor‘eastern high opening bottom trawls rigged with roller gear. In a full three-boat survey, 800 tows are completed, but the recent average has been closer to 600 tows. On average, 72% of these tows contain pollock (Table 1.8). Recent years have dropped stations in deeper water which are unlikely to affect the index due to pollock typically being in shallower depths with on average 90.9% below 200 m and 99.6% below 300 m from 1984-2021.

Biomass Estimates

The time series of pollock biomass used in the assessment model is based on the surveyed area in the Gulf of Alaska west of 140° W long., obtained by adding the biomass estimates for the Shumagin-610, Chirikof-620, Kodiak-630 statistical areas, and the western portion of Yakutat-640 statistical area. Biomass estimates for the west Yakutat area were obtained by splitting strata and survey CPUE data at 140° W long. and re-estimating biomass for west Yakutat. In 2001, when eastern Gulf of Alaska was not surveyed, a random effects model was used to interpolate a value for west Yakutat for use in the assessment model.

The Alaska Fisheries Science Center’s (AFSC) Resource Assessment and Conservation Engineering (RACE) Division conducted the seventeenth comprehensive bottom trawl survey since 1984 during the summer of 2021 (Fig. 1.4). The 2021 gulfwide biomass estimate of pollock was 528,841 t, which is an increase of 72.2% from the 2019 estimate, which was the second lowest in the time series after 2001. The biomass estimate for the portion of the Gulf of Alaska west of 140º W long. used in the assessment model is 494,743 t. The coefficient of variation (CV) of this estimate was 0.17, which is slightly below the average for the entire time series. Surveys from 1990 onwards are used in the assessment due to the difficulty in standardizing the surveys in 1984 and 1987, when Japanese vessels with different gear were used.

Age Composition

Estimates of numbers at age from the bottom trawl survey are obtained from random otolith samples and length frequency samples (Table 1.9). Numbers at age are estimated by statistical area (Shumagin-610, Chirikof-620, Kodiak-630, Yakutat-640 and Southeastern-650) using a global age-length key for all strata in each single year, and CPUE-weighted length frequency data by statistical area. The combined Shumagin, Chirikof and Kodiak age composition is used in the assessment model (Fig. 1.4). No new ages were available this year, and instead length compositions were used in the model (Fig. 1.5) but 2019 ages indicated the continued dominance of the 2012 year class (age-7 fish) in the Western and Central GOA (Fig. 1.6). Age-1 pollock were strongly present in the Chirikof, Kodiak, and Yakutat statistical areas, but much less abundant in the Shumagin and Southeast Alaska areas (Fig. 1.7).

Shelikof Strait Acoustic Survey

Winter acoustic surveys to assess the biomass of pre-spawning aggregations pollock in Shelikof Strait have been conducted annually since 1981 (except 1982, 1999, and 2011). Only surveys from 1992 and later are used in the stock assessment due to the higher uncertainty associated with the acoustic estimates produced with the Biosonics echosounder used prior to 1992. Additionally, raw survey data are not easily recoverable for the earlier acoustic surveys, so there is no way to verify (i.e., to reproduce) the estimates. Survey methods and results for 2021 are presented in a NMFS processed report (Honkalehto et al., in prep.). In 2008, the noise-reduced R/V Oscar Dyson became the designated survey vessel for acoustic surveys in the Gulf of Alaska. In winter of 2007, a vessel comparison experiment was conducted between the R/V Miller Freeman (MF) and the R/V Oscar Dyson (OD), which obtained an OD/MF ratio of 1.132 for the acoustic backscatter detected by the two vessels in Shelikof Strait.

Biomass Estimates

The 2021 biomass estimate for Shelikof Strait is 526,974 t, which is a 15% percent increase from the 2020 estimate (Fig. 1.8). This estimate accounts for trawl selectivity by scaling up the number of retained pollock by selectivity curves estimated with pocket nets attached to the midwater trawl used to sample echosign, continuing an approach that was started in 2018 assessment. Originally, winter 2021 pre-spawning pollock surveys were also planned in the Shumagin Islands area, Chirikof shelf break, and in Prince William Sound and the Kenai Peninsula fjords. Due to travel, vessel, and staffing constraints stemming from protocols required to mitigate the COVID-19 pandemic, only Shelikof, Marmot, and Chirikof were attempted. Eventually Chirikof was dropped due to inclement weather and because real-time observations of the large age-1 2020 year class in Shelikof Strait necessitated collecting sufficient additional trawling to estimate net selectivity for pollock in 2021

table TODO

Biomass in Marmot Bay in 2021 increased by 18% compared to 2019, the last year it was surveyed. Overall, there appears to be a concentration of spawning activity in Shelikof Strait compared to other areas in the Gulf of Alaska, but the reduced survey coverage outside of Shelikof Strait limits the conclusions that can be drawn.

Age Composition

Estimates of numbers at age from the Shelikof Strait acoustic survey (Table 1.10, Fig. 1.9) were obtained using an age-length key compiled from random otolith samples and applied to weighted length frequency samples. Sample sizes for ages and lengths are given Table 1.11. Estimates of age composition in Shelikof Strait in 2021 indicate reduced dominance of the nine year old 2012 year class, and a mode of age 4 fish (2017 year class), indicating a new year class is starting to comprise the majority of the spawning and exploitable portion of the population.

Based on recommendations from the 2012 CIE review, we developed an approach to model the age-1 and age-2 pollock estimates separately from the Shelikof Strait acoustic survey biomass and age composition. Age-1 and age-2 pollock are highly variable but occasionally very abundant in winter acoustic surveys, and by fitting them separately from the 3+ fish it is possible utilize an error distribution that better reflects that variability. Indices are available for both the Shelikof Strait and Shumagin surveys, but a longer time series of net-selectivity corrected indices are available for Shelikof Strait. In addition, model comparisons in the 2018 assessment indicates that a slightly better fit could be obtained with only Shelikof Strait indices. Therefore this time series was used in the model, but this decision should be revisited as additional data become available. The age-2 index in 2020 showed a marked reduction in comparison to the age-1 index in 2019, which indicated high abundance of the 2018 year class. Typically year classes that are abundant in Shelikof Strait at age 1 are also abundant at age 2 in the survey in the following year. The 2018 cohort comprised 15% of the age composition (excluding age 1 and 2 fish) as 3 year olds in 2021, giving further evidence for marked decrease from initial estimates as age 1 fish. Consequently, there is considerable uncertainty regarding the fate of 2018 year class, which may have exited Shelikof Strait for some reason and be distributed elsewhere in the GOA, or suffered extremely high mortality.

Spawn timing and availability of pollock to the winter Shelikof survey

The Shelikof Strait winter acoustic survey is timed to correspond to the aggregation of pre-spawning pollock in Shelikof Strait. However, the timing of spawning has been found to vary from year to year, which may affect the availability of pollock to the survey. Variation in spawn timing is not random, but has been linked to thermal conditions in March and the age structure of the spawning stock (Rogers and Dougherty 2019); spawning tends to occur earlier when temperatures are warmer and when the spawning stock is older on average. Greater age diversity also results in a more protracted spawning period, presumably due to both early (old) and late (young) spawners, although this has not been verified in the field. Dorn et al. (2020) discuss correlations with spawn timing and model residuals. No additional work was done this year but is an ongoing effort.

Summer Acoustic Survey

Five complete acoustic surveys, in 2013, 2015, 2017, 2019 and 2021, have been conducted by AFSC on the R/V Oscar Dyson in the Gulf of Alaska during summer (Jones et al. 2014, 2017, 2019, in prep.; Levine et al. in prep.). The area surveyed covers the Gulf of Alaska shelf and upper slope and associated bays and troughs, from a westward extent of 170° W Lon, and extends to an eastward extent of 140° W lon. Prince William Sound was also surveyed in 2013, 2015, and 2019. The survey consists of widely-spaced parallel transects along the shelf, and more closely spaced transects in troughs, bays, and Shelikof Strait. Mid-water and bottom trawls are used to identify acoustic targets. The 2021 biomass estimate for summer acoustic survey is 431,148 t, which is a 25% percent decrease from the 2019 estimate (Table 1.7). Age composition data were not available, but preliminary results in 2021 indicated that the very abundant 2012 year class was present but with reduced contribution, and strong modes of both presumed age-1 and age-4 fish were distributed broadly throughout the GOA (Fig. 1.10). Analysis of the 2019 and 2021 survey was not complicated by the presence of age-0 pollock, which was a problem in previous summer acoustic surveys because age-0 pollock backscatter cannot be readily distinguished from age 1+ pollock.

Alaska Department of Fish and Game Crab/Groundfish Trawl Survey

The Alaska Department of Fish and Game (ADF&G) has conducted bottom trawl surveys of nearshore areas of the Gulf of Alaska since 1987 (depths from 18-246 m, median of 106 m; Fig. 1.11). Although these surveys are designed to monitor population trends of Tanner crab and red king crab, pollock and other fish are also sampled. Standardized survey methods using a 400-mesh eastern trawl were employed from 1987 to the present. The survey is designed to sample at fixed stations from mostly nearshore areas from Kodiak Island to Unimak Pass, and does not cover the entire shelf area (Fig. 1.11). The average number of tows completed during the survey is 337. On average, 87% of these tows contain pollock. Details of the ADF&G trawl gear and sampling procedures are in Spalinger (2012).

The 2021 area-swept biomass estimate for pollock for the ADF&G crab/groundfish survey was 64,813 t, and increase of 9.2% from the 2020 biomass estimate (Table 1.7). The 2021 pollock estimate for this survey is approximately 70% of the long-term average. ### Biomass Estimates A simple delta GLM model was applied to the ADF&G tow by tow data for 1988-2021 to obtain annual abundance indices. Data from all years were filtered to exclude missing latitude and longitudes and missing tows made in lower Shelikof Strait (between 154.7° W lon. and 156.7° W lon.) were excluded because these stations were sampled irregularly. The delta GLM model fit a separate model to the presence-absence observations and to the positive observations. A fixed effects model was used with the year, geographic area, and depth as factors. Strata were defined according to ADF&G district (Kodiak, Chignik, South Peninsula) and depth (<30 fm, 30-100 fm, >100 fm). Alternative depth strata were evaluated, and model results were found to be robust to different depth strata assumptions. The same model structure was used for both the presence-absence observations and the positive observations. The assumed likelihoods were binomial for presence-absence observations and gamma for the positive observations, after evaluation of several alternatives, including lognormal, gamma, and inverse Gaussian, and which is in line with recommendations for index standardization (Thorson et al. 2021). The model was fit using brms package in R (Bürkner 2017, 2018), which fits Bayesian non-linear regression models using the modeling framework Stan (Stan Development Team 2020). Comparison of delta-GLM indices the area-swept estimates indicated similar trends (Fig. 1.12). Variances were based on MCMC sampling from the posterior distribution, and CVs for the annual index ranged from 0.10 to 0.18. These values likely understate the uncertainty of the indices with respect to population trends, since the area covered by the survey is a relatively small percentage of the GOA shelf area, and so the CVs are scaled up to have an average of 0.25.

Age Compositions

Ages were determined by age readers in the AFSC age and growth unit from samples of pollock otoliths collected during 2000-2020 ADF&G surveys in even-numbered years (average sample size = 583; Table 1.12, Fig. 1.13). Comparison with fishery age composition shows that older fish (> age-8) are more common in the ADF&G crab/groundfish survey. This is consistent with the assessment model, which estimates a domed-shaped selectivity pattern for the fishery, but an asymptotic selectivity pattern for the ADF&G survey.

Data sets considered but not used

Egg production estimates of spawning biomass

Estimates of spawning biomass in Shelikof Strait based on egg production methods were produced during 1981-92 (Table 1.7). A complete description of the estimation process is given in Picquelle and Megrey (1993). Egg production estimates were discontinued in 1992 because the Shelikof Strait acoustic survey provided similar information. The egg production estimates are not used in the assessment model because the surveys are no longer being conducted, and because the acoustic surveys in Shelikof Strait show a similar trend over the period when both were conducted.

Pre-1984 bottom trawl surveys

Considerable survey work was carried out in the Gulf of Alaska prior to the start of the NMFS triennial bottom trawl surveys in 1984. Between 1961 and the mid-1980s, the most common bottom trawl used for surveying was the 400-mesh eastern trawl. This trawl (or variants thereof) was used by IPHC for juvenile halibut surveys in the 1960s, 1970s, and early 1980s, and by NMFS for groundfish surveys in the 1970s. Von Szalay and Brown (2001) estimated a fishing power correction (FPC) for the ADF&G 400-mesh eastern trawl of 3.84 (SE = 1.26), indicating that 400-mesh eastern trawl CPUE for pollock would need to be multiplied by this factor to be comparable to the NMFS poly-Nor’eastern trawl.

In most cases, earlier surveys in the Gulf of Alaska were not designed to be comprehensive, with the general strategy being to cover the Gulf of Alaska west of Cape Spencer over a period of years, or to survey a large area to obtain an index for group of groundfish, i.e., flatfish or rockfish. For example, Ronholt et al. (1978) combined surveys for several years to obtain gulfwide estimates of pollock biomass for 1973-1976. There are several difficulties with such an approach, including the possibility of double-counting or missing a portion of the stock that happened to migrate between surveyed areas. Due to the difficulty in constructing a consistent time series, the historical survey estimates are no longer used in the assessment model.

Multi-year combined survey estimates indicate a large increase in pollock biomass in the Gulf of Alaska occurred between the early 1960s and the mid 1970s. Increases in pollock biomass between the1960s and 1970s were also noted by Alton et al. (1987). In the 1961 survey, pollock were a relatively minor component of the groundfish community with a mean CPUE of 16 kg/hr. (Ronholt et al. 1978). Arrowtooth flounder was the most common groundfish with a mean CPUE of 91 kg/hr. In the 1973-76 surveys, the CPUE of arrowtooth flounder was similar to the 1961 survey (83 kg/hr.), but pollock CPUE had increased 20-fold to 321 kg/hr., and was by far the dominant groundfish species in the Gulf of Alaska. Mueter and Norcross (2002) also found that pollock was low in the relative abundance in 1960s, became the dominant species in Gulf of Alaska groundfish community in the 1970s, and subsequently declined in relative abundance.

Questions concerning the comparability of pollock CPUE data from historical trawl surveys with later surveys probably can never be fully resolved. However, because of the large magnitude of the change in CPUE between the surveys in the 1960s and the early 1970s using similar trawling gear, the conclusion that there was a large increase in pollock biomass seems robust. Early speculation about the rise of pollock in the Gulf of Alaska in the early 1970s implicated the large biomass removals of Pacific ocean perch, a potential competitor for euphausid prey (Somerton 1979, Alton et al. 1987). More recent work has focused on role of climate change (Anderson and Piatt 1999, Bailey 2000). These easrlier surveys suggest that population biomass in the 1960s, prior to large-scale commercial exploitation of the stock, may have been lower than at any time since then.

Qualitative Trends

To qualitatively assess recent trends in abundance, each survey time series was standardized by dividing the annual estimate by the average since 1990. Shelikof Strait acoustic survey estimates prior to 2008 were rescaled to be comparable to subsequent surveys conducted by the R/V Oscar Dyson. Although there is considerable variability in each survey time series, a fairly clear downward trend is evident to 2000, followed by a stable, though variable, trend to 2008, followed by a strong increase to 2013 (Fig. 1.14). From 2016 to 2019 there was a strong divergence among the trends, but with the large reduction in biomass in 2020 for the Shelikof Strait survey, and an increase in the ADF&G index, relative abundance has come back into reasonable alignment since 2020. Indices derived from fisheries catch data were also evaluated for trends in biological characteristics (Fig. 1.15). The percent of females in the catch shows some variability but no obvious trend, and is usually close to 50-50. In 2016, percent female dropped to 40%, but increased to 43% in 2017 and remained similar through 2020. Evaluation of sex ratios by season indicated that this decrease was mostly due a low percentage of females during the A and B seasons prior to spawning. However the sex ratio during the C and D seasons was close to 50-50, suggesting the skewed sex in winter was related to spawning behavior, rather than an indication of a population characteristic. The mean age shows interannual variability due to strong year classes passing through the population, but there are no downward trends that would suggest excessive mortality rates. The percent of old fish in the catch (nominally defined as age 8 and older) is also highly variable due to variability in year class strength. The percent of old fish declined in 2015-2018 as the strong 2012 year class recruited to the fishery, but increased when the 2012 year class became age 8 in 2020. Under a constant F40% harvest rate, the mean percent of age 8 and older fish in the catch would be approximately 8%. An annual index of catch at age diversity was computed using the Shannon-Wiener information index,

\[ -\sum_a{ p_a \ln {p_a}} \]

where \(p_a\) is the proportion at age and higher values correspond to higher diversity. Increases in fishing mortality would tend to reduce age diversity, but year class variability would also influence it. Age diversity was relatively stable during 1975-2015, but declined sharply to a low in 2016 and has been increasing since due to the dominance of the 2012 year class in the catch (Fig. 1.15). In 2020 the age diversity returned to near the long-term average.

The 2012 year class, which is both very strong, and which has experienced anomalous environmental conditions during the marine heatwave in the North Pacific during 2015-2017, has displayed unusual life history characteristics. These include early maturation, reduced growth, but apparently not reduced total mortality (Fig. 1.16). It is unclear whether these changes are a result of density dependence or environmental forcing.

Analytical approach

General Model Structure

An age-structured model covering the period from 1970 to 2021 (52 years) was used to assess Gulf of Alaska pollock. The modeled population includes individuals from age 1 to age 10, with age 10 defined as a “plus” group, i.e., all individuals age 10 and older. Population dynamics were modeled using standard formulations for mortality and fishery catch (e.g. Fournier and Archibald 1982, Deriso et al. 1985, Hilborn and Walters 1992). Year- and age-specific fishing mortality was modeled as a product of a year effect, representing the full-selection fishing mortality, and an age effect, representing the selectivity of that age group to the fishery. The age effect was modeled using a double-logistic function with time-varying parameters (Dorn and Methot 1990, Sullivan et al. 1997). The model was fit to time series of catch biomass, survey indices of abundance, and estimates of age and length composition from the fishery and surveys. Details of the population dynamics and estimation equations are presented in Appendix 1C.

Model parameters were estimated by maximizing the joint log likelihood of the data, viewed as a function of the parameters. Mean-unbiased log-normal likelihoods were used for survey biomass and total catch estimates, and multinomial likelihoods were used for age and length composition data. Model tuning for composition data was done by iterative re-weighting of input sample sizes using the Francis (2011) method. Variance estimates/assumptions for survey indices were not reweighted. The following table lists the likelihood components used in fitting the model.

table of likelihoods TODO

Recruitment

In most years, year-class abundance at age 1 was estimated as a free parameter. Age composition in the first year was estimated with a single log deviation for recruitment abundance, which was then decremented by natural mortality to fill out the initial age vector. A penalty was added to the log likelihood so that the log deviation in recruitment for 1970-77, and in the last two years of the model, would have the same variability as recruitment during the data-rich period (\(\sigma_R =1.0\)). Log deviations from mean log recruitment were estimated as free parameters in other years. These relatively weak constraints were sufficient to obtain fully converged parameter estimates while retaining an appropriate level of uncertainty.

Modeling fishery data

To accommodate changes in selectivity we estimated year-specific parameters for the slope and the intercept parameter for the ascending logistic portion of selectivity curve (i.e., younger fish). Variation in these parameters was constrained using a random walk penalty.

Modeling survey data

Survey abundance was assumed to be proportional to total abundance as modified by the estimated survey selectivity pattern. Expected population numbers at age for the survey were based on the mid-date of the survey, assuming constant fishing and natural mortality throughout the year. Standard deviations in the log-normal likelihood were set equal to the sampling error CV (coefficient of variation) associated with each survey estimate of abundance (Kimura 1991).

Survey catchability coefficients can be fixed or freely estimated. The base model estimated the NMFS bottom trawl survey catchability, but used a log normal prior with a median of 0.85 and log standard deviation 0.1 based on expert judgement as a constraint on potential values (Fig. 1.17). Catchability coefficients for other surveys were estimated as free parameters. The age-1 and age-2 winter acoustic survey indices are numerical abundance estimates, and were modeled using independently estimated catchability coefficients (i.e., no selectivity is estimated).

This assessment is based on a statistical age-structured model with the catch equation and population dynamics model as described in (Fournier1982?) and elsewhere (e.g., (Hilborn1992?); (Schnute1995?), (McAllister1997?)). The catch in numbers at age in year \(t (C_{t,a})\) and total catch biomass \((Y_t)\) can be described as:

A vessel comparison (VC) experiment was conducted in March 2007 during the Shelikof Strait acoustic survey. The VC experiment involved the R/V Miller Freeman (MF, the survey vessel used to conduct Shelikof Strait surveys since the mid-1980s), and the R/V Oscar Dyson (OD), a noise-reduced survey vessel designed to conduct surveys that have traditionally been done with the R/V Miller Freeman. The vessel comparison experiment was designed to collect data either with the two vessels running beside one another at a distance of 0.7 nmi, or with one vessel following nearly directly behind the other at a distance of about 1 nmi. The methods were similar to those used during the 2006 Bering Sea VC experiment (De Robertis et al. 2008). Results indicate that the ratio of 38 kHz pollock backscatter from the R/V Oscar Dyson relative to the R/V Miller Freeman was significantly greater than one (1.13), as would be expected if the quieter OD reduced the avoidance response of the fish. Previously we included a likelihood component to incorporate this information in the assessment model, but dropped it because this survey is now modeled with a random walk in catchability, and a relatively small systematic change in catchability is inconsequential compared to other factors affecting catchability.

Ageing error

An ageing error conversion matrix is used in the assessment model to translate model population numbers at age to expected fishery and survey catch at age (Table 1.13). Dorn et al. (2003) estimated this matrix using an ageing error model fit to the observed percent reader agreement at ages 2 and 9. Mean percent agreement is close to 100% at age 1 and declines to 40% at age 10. Annual estimates of percent agreement are variable, but show no obvious trend; hence a single conversion matrix for all years in the assessment model was adopted. The model is based on a linear increase in the standard deviation of ageing error and the assumption that ageing error is normally distributed. The model predicts percent agreement by taking into account the probability that both readers are correct, both readers are off by one year in the same direction, and both readers are off by two years in the same direction (Methot 2000). The probability that both agree and were off by more than two years was considered negligible. A study evaluated pollock ageing criteria using radiometric methods and found them to be unbiased (Kastelle and Kimura 2006).

Length frequency data

The assessment model was fit to length frequency data from various sources by converting predicted age distributions (as modified by age-specific selectivity) to predicted length distributions using an age-length conversion matrix. This approach was used only when age composition estimates were unavailable, as occurs when the survey is the same as the assessment. Because seasonal differences in pollock length at age are large, particularly for the younger fish, several conversion matrices were used. For each matrix, unbiased length distributions at age were estimated for several years using age-length keys, and then averaged across years. A conversion matrix was estimated using 1992-1998 Shelikof Strait acoustic survey data and used for winter survey length frequency data. The following length bins were used: 5-16, 17 - 27, 28 - 35, 36 - 42, 43 - 50, 51 - 55, 56 - 70 (cm). Age data for the most recent survey is now routinely available so this option does not need to be invoked. A conversion matrix was estimated using second and third trimester fishery age and length data during the years (1989-1998), and was used when age composition data are unavailable for the summer bottom trawl survey, which is only for the most recent survey in the year that the survey is conducted. The following length bins were used: 5-24, 25 - 34, 35 - 41, 42 - 45, 46 - 50, 51 - 55, 56 – 70 (cm), so that the first four bins would capture most of the summer length distribution of the age-1, age-2, age-3 and age-4 fish, respectively. Bin definitions were different for the summer and the winter conversion matrices to account for the seasonal growth of the younger fish (ages 1-4).

Initial data weighting

The input sample sizes were initially standardized by data set before model tuning. Fishery age composition was given an initial sample size of 200 except when the age sample in a given year came from fewer than 200 hauls/deliveries, in which case the number of hauls/deliveries was used. Both the Shelikof acoustic survey and the bottom trawl were given an initial sample size of 60, and the ADF&G crab/groundfish survey was given a weight of 30.

Parameters Estimated Outside the Assessment Model

Pollock life history characteristics, including natural mortality, weight at age, and maturity at age, were estimated independently outside the assessment model. These parameters are used in the model to estimate spawning and population biomass and obtain predictions of fishery catch and survey biomass. Pollock life history parameters include:

-Natural mortality (M) -Proportion mature at age -Weight at age and year by fishery and by survey

Natural mortality

Hollowed and Megrey (1990) estimated natural mortality (M) using a variety of methods including estimates based on: a) growth parameters (Alverson and Carney 1975, and Pauly 1980), b) GSI (Gunderson and Dygert, 1988), c) monitoring cohort abundance, and d) estimation in the assessment model. These methods produced estimates of natural mortality that ranged from 0.22 to 0.45. The maximum age observed was 22 years. Up until the 2014 assessment, natural mortality had been assumed to be 0.3 for all ages.

Hollowed et al. (2000) developed a model for Gulf of Alaska pollock that accounted for predation mortality. The model suggested that natural mortality declines from 0.8 at age 2 to 0.4 at age 5, and then remains relatively stable with increasing age. In addition, stock size was higher when predation mortality was included. In a simulation study, Clark (1999) evaluated the effect of an erroneous M on both estimated abundance and target harvest rates for a simple age-structured model. He found that “errors in estimated abundance and target harvest rate were always in the same direction, with the result that, in the short term, extremely high exploitation rates can be recommended (unintentionally) in cases where the natural mortality rate is overestimated and historical exploitation rates in the catch-at-age data are low.” Clark (1999) proposed that the chance of this occurring could be reduced by using an estimate of natural mortality on the lower end of the credible range, which is the approach used in this assessment. In the 2014 assessment, several methods to estimate of the age-specific pattern of natural mortality were evaluated. Two general types of methods were used, both of which are external to the assessment model. The first type of method is based initially on theoretical life history or ecological relationships that are then evaluated using meta-analysis, resulting in an empirical equation that relates natural mortality to some more easily measured quantity such as length or weight. The second type of method is an age-structured statistical analysis using a multispecies model or single species model where predation is modeled. There are three examples of such models for pollock in Gulf of Alaska, a single species model with predation by Hollowed et al. (2000), and two multispecies models that included pollock by Van Kirk et al. (2010 and 2012). These models were published in the peer-reviewed literature, but likely did not receive the same level of scrutiny as stock assessment models. Although these models also estimate time-varying mortality, we averaged the total mortality (residual natural mortality plus predation mortality) for the last decade in the model to obtain a mean age-specific pattern (in some cases omitting the final year when estimates were much different than previous years). Use of the last decade was an attempt to use estimates with the strongest support from the data. Approaches for inclusion of time-varying natural mortality will be considered in future pollock assessments. The three theoretical/empirical methods used were the following:

Brodziak et al. 2011: Age-specific M is given by

\[\begin{equation*} M(a)= \begin{cases} M_c \frac{L_{mat}}{L(a)} & \text{for } a<a_{mat}\\ M_c & \text{for } a \geq a_{mat} \end{cases} \end{equation*}\]

where \(L_{mat}\) is the length at maturity, \(M_c=0.30\) is the natural mortality at \(L_{mat}\), \(L(a)\) is the mean length at age for the summer bottom trawl survey for 1984-2013.

Lorenzen 1996: Age-specific M for ocean ecosystems is given by

\[ M(a)=\bar{W_a}^{-0.305}\]

where \(\bar{W_a}\) is the mean weight at age from the summer bottom trawl survey for 1984-2013.

Gislason et al. 2010: Age-specific M is given by

\[\ln(M)=0.55-1.61\ln(L)+1.44\ln(L_{\infty})+\ln{K}\] where \(L_\infty = 65.2\) cm and \(K = 0.30\) were estimated by fitting von Bertalanffy growth curves using the NLS routine in R using summer bottom trawl age data for 2005-2009 for sexes combined in the central and western Gulf of Alaska. Results were reasonably consistent and suggest use of a higher mortality rate for age classes younger than the age at maturity (Table 1.14 and Fig. 1.18). Somewhat surprisingly, the theoretical/empirical estimates were similar, on average, to predation model estimates. To obtain an age-specific natural mortality schedule for use in the stock assessment, we used an ensemble approach and averaged the results for all methods. Then we used the method recommended by Clay Porch in Brodziak et al (2011) to rescale the age-specific values so that the average for range of ages equals a specified value. Age-specific values were rescaled so that a natural mortality for fish greater than or equal to age 5, the age at 50% maturity, was equal to 0.3, the value of natural mortality used in previous pollock assessments.

Maturity at age

Maturity stages for female pollock describe a continuous process of ovarian development between immature and post-spawning. For the purposes of estimating a maturity vector (the proportion of an age group that has been or will be reproductively active during the year) for stock assessment, all fish greater than or equal to a particular maturity stage are assumed to be mature, while those less than that stage are assumed to be immature. Maturity stages in which ovarian development had progressed to the point where ova were distinctly visible were assumed to be mature (i.e., stage 3 in the 5-stage pollock maturity scale). Maturity stages are qualitative rather than quantitative, so there is subjectivity in assigning stages, and a potential for different technicians to apply criteria differently (Neidetcher et al. 2014). Because the link between pre-spawning maturity stages and eventual reproductive activity later in the season is not well established, the division between mature and immature stages is problematic. Changes in the timing of spawning could also affect maturity at age estimates. Merati (1993) compared visual maturity stages with ovary histology and a blood assay for vitellogenin and found general consistency between the different approaches. Merati (1993) noted that ovaries classified as late developing stage (i.e., immature) may contain yolked eggs, but it was unclear whether these fish would have spawned later in the year. The average sample size of female pollock maturity stage data per year since 2000 from winter acoustic surveys in the Gulf of Alaska is 373 (Table 1.15). In 2019, a new approach was introduced to estimate maturity at age using specimen data from the Shelikof Strait acoustic survey. Maturity estimates from 2003 onwards were revised using this method. The approach uses local abundance to weight the maturity data collected in a haul. To estimate abundance, each acoustic survey distance unit (0.5 nmi of trackline) was assigned to a stratum representing nearest survey haul. Each haul’s biological data was then used to scale the corresponding acoustic backscatter by within that stratum into abundance. To generate abundance weights for specimen data taken for each haul location, the abundance estimates of adult pollock (\(\geq 30\) cm fork length) were summed for each haul-stratum. The 30 cm length threshold represents the length at which pollock are 5% mature in the entire Shelikof Strait historic survey data. Total adult pollock abundances in each stratum scaled by dividing by the mean abundance per stratum (total abundance /number of haul-strata). Weights range from 0.05 to 6, as some hauls were placed in light sign while others sampled very dense aggregations. For each haul, the number of female pollock considered mature (prespawning, spawning, or spent) and immature (immature or developing) were computed for each age. The maturity ogive for maturity-at-age was estimated as a logistic regression using a weighted generalized linear model where the dependent variable was the binomial spawning state, the independent variable was the age, and data from each haul weighted by the appropriate values as computed above. The length and age at 50% maturity was derived (L50%, A50%) from the ratio of the regression coefficients. The new maturity estimates had a relatively minor impact on assessment results, and usually reduced estimates of spawning biomass by about 2 percent. Estimates of maturity at age in 2021 from winter acoustic surveys using the new method are higher for younger fish, but lower for older fish, compared to 2020 and the long-term mean for all ages (Fig. 1.19). Inter-annual changes in maturity at age may reflect environmental conditions, pollock population biology, effect of strong year classes moving through the population, or simply ageing error. Because there did not appear to be an objective basis for excluding data, the 1983-2021 average maturity at age was used in the assessment.

Logistic regression (McCullagh and Nelder 1983) was also used to estimate the age and length at 50% maturity at age for each year to evaluate long-term changes in maturation. Annual estimates of age at 50% maturity are highly variable and range from 2.6 years in 2017 to 6.1 years in 1991, with an average of 4.8 years (Fig. 1.20). The last few years has shown a decrease in the age at 50% mature, which is largely being driven by the maturation of the 2012 year class at younger ages than is typical, however the 2019 to 2021 estimates of age at 50% mature are near the long-term average. Length at 50% mature is less variable than the age at 50% mature, suggesting that at least some of the variability in the age at maturity can be attributed to changes in length at age. Changes in year-class dominance also likely affect estimates of maturity at length, as a similar pattern is seen as with maturity at age with the 2012 cohort . The average length at 50% mature for all years is approximately 43 cm.

Weight at age

Year-specific fishery weight-at-age estimates are used in the model to obtain expected catches in biomass. Where possible, year and survey-specific weight-at-age estimates are used to obtain expected survey biomass. For each data source, unbiased estimates of length at age were obtained using year-specific age-length keys. Bias-corrected parameters for the length-weight relationship, \(W=aL^b\) , were also estimated. Weights at age were estimated by multiplying length at age by the predicted weight based on the length-weight regressions. Weight at age for the fishery, the Shelikof Strait acoustic survey, and the NMFS bottom trawl survey and the summer acoustic survey are given in Table 1.16, Table 1.17, and Table 1.18. Data from the Shelikof Strait acoustic survey indicates that there has been a substantial changes in weight at age for older pollock (Fig. 1.21). For pollock greater than age 6, weight-at-age nearly doubled by 2012 compared to 1983-1990. However, weight at age since 2012 has trended strongly downward, with some stabilization in the last couple of years, but a notable increase in 2021 for all ages, and the heaviest age 2 fish to date (0.191 kg) and fourth heaviest age 3 fish (0.321 kg) as well. Further analyses are needed to evaluate whether these changes are a density-dependent response to declining pollock abundance, or whether they are environmentally forced. Changes in weight-at-age have potential implications for status determination and harvest control rules.

A random effects (RE) model for weight at age (Ianelli et al. 2016) was used to estimate of fishery weight at age in 2021 since age data were not available. The structural part of the model is an underlying von Bertalanffy growth curve. Year and cohort effects are estimated as random effects using the ADMB RE module. Further details are provided in Ianelli et al. (2016). Input data included fishery weight age for 1975-2020. The model also incorporates survey data by modeling an offset between fishery and survey weight at age. Weight at age for the Shelikof Strait acoustic survey (1981-2021) and the NMFS bottom trawl survey (1984-2019) were used. The model also requires input standard deviations for the weight at age data, which are not available for GOA pollock. In the 2016 assessment, a generalized variance function was developed using a quadratic curve to match the mean standard deviations at ages 3-10 for the eastern Bering Sea pollock data. The standard deviation at age one was assumed to be equal to the standard deviation at age 10. Survey weights at age were assumed to have standard deviations that were 1.5 times the fishery weights at age. A comparison of RE model estimates from last year of the 2020 fishery weight at age with the data now available indicate that the model underestimated weights except for ages 9-10 (Fig. 1.22). This includes underestimates of the age 3 and 8 fish in 2020 which made up the majority of catch (36% and 31%, respectively). In this assessment, RE model estimates of weight at age are used for the fishery in 2021 and for yield projections (Fig. 1.22).

Parameters Estimated Inside the Assessment Model

A large number of parameters are estimated when using this modeling approach, though many are year-specific deviations in fishery selectivity coefficients. Parameters were estimated using AD Model Builder (Version 12.3), a C++ software language extension and automatic differentiation library (Fournier et al. 2012). Parameters in nonlinear models are estimated in AD Model Builder using automatic differentiation software extended from Greiwank and Corliss (1991) and developed into C++ class libraries. The optimizer in AD Model Builder is a quasi-Newton routine (Press et al. 1992). The model is determined to have converged when the maximum parameter gradient is less than a small constant (set to 1 x 10-6) and the Hessian matrix is invertible. AD Model Builder includes post-convergence routines to calculate standard errors (or likelihood profiles) for any quantity of interest.

A list of model parameters for the base model is shown below:

Description of Alternative Models

Description of alternative models included in the assessment, if any (e.g., alternative M values or likelihood weights); note that the base model (i.e., the model most recently accepted by the SSC, either after reviewing the previous year’s final assessment or the current year’s preliminary assessment) must be included Per recommendation of the SSC (10/15), please use the following convention for numbering models: When a model constituting a “major change” from the original version of the base model is introduced, it is given a label of the form “Model yy.j,” where yy is the year (designated by the last two digits) that the model was introduced, and j is an integer distinguishing this particular “major change” model from other “major change” models introduced in the same year. When a model constituting only a “minor change” from the original version of the base model is introduced, it is given a label of the form “Model yy.jx,” where x is a letter distinguishing this particular “minor change” model from other “minor change” models derived from the original version of the same base model. Specifically, please use one of the following four options to distinguish “major” from “minor” changes:

Results

Model selection and evaluation

Model selection

Prior to identifying a model for consideration, an analysis was conducted of the impact of each new data element on model results. Figure 1.21 shows the changes in estimated spawning biomass as the updated catch projections, catch at age, and surveys were added sequentially. In general, the addition of new data elements did not strongly affect the estimates of recent spawning biomass, with the exception of the updated weight at age from the 2021 Shelikof survey, which was substantially larger than the 2020 estimates. This effect is discussed in the risk table below. This suggests that the new data are reasonably consistent with previous modeling and with each other. Since previous assessments have identified inconsistent input data sets as a major assessment concern, the overall consistency this year suggests that those concerns are much reduced (e.g., Fig. 1.23).

The intent of this year’s assessment was to provide a straightforward update without considering major changes to the model. We recently explored models that used VAST estimates in place of area-swept biomass estimates for the NMFS bottom trawl survey. The VAST estimates did not fit as well as the area-swept estimates when given similar weighting, and we concluded that additional model evaluation was needed before using the VAST estimates. Several other modeling approaches for GOA pollock are under development, including incorporation of predator consumption (Barnes et al. 2020) in the assessment model, use of mean hatch date from the EcoFOFI early larval survey to inform catchability to the Shelikof Strait survey, and model-based estimates of Shelikof and summer acoustic indices using VAST. We selected model 19.1 as the preferred model, and a final turning step was done using the Francis (2011) approach which reweighted all composition components, including the summer acoustic age composition for the first time, but model results were nearly unchanged (Fig. 1.23).

Model evaluation

The fit of model 19.1 to age composition data was evaluated using plots of observed and predicted age composition and residual plots. Figure 1.24 show the estimates of time-varying catchability for the Shelikof Strait acoustic survey and the ADF&G crab/groundfish survey. The catchability for the Shelikof Strait acoustic survey approaches one but does not exceed it and has declined in the last two years. Plots show the fit to fishery age composition (Fig. 1.25, Fig. 1.26), Shelikof Strait acoustic survey age composition (Fig. 1.27, Fig. 1.28), NMFS trawl survey age composition (Fig. 1.29), and ADF&G trawl survey age composition (Fig. 1.30). Model fits to fishery age composition data are adequate in most years, though the very strong 2012 year class shows up as a positive residual in for the 2016-2019 due to stronger than expected abundance in the age composition, while the older ages tended to have negative residuals. This may indicate that the fishery is targeting on the 2012 year class. The largest residuals tended to be at ages 1-2 in the NMFS bottom trawl survey due to inconsistencies between the initial estimates of abundance and subsequent information about year class size.

The fit to the 2021 Shelikof survey age was notably poor with a very large negative residual for age 3 fish (Fig. 1.27). A similar pattern is observed in the 2020 age 2 residual for the ADF&G compositional data (Fig. 1.30). These both point to a smaller 2018 cohort than originally observed and estimated. However, the fit to age 2 fish in the 2020 fishery data is much better, potentially due to lower selectivity at that age, and that it is time varying. Consequently, there is still conflict and uncertainty in the data about the size of the 2018 cohort. We anticipate new age composition data for the 2021 fishery, NMFS bottom trawl and summer acoustic surveys, and 2022 Shelikof survey to shed further light on the fate of this cohort.

Model fits to survey biomass estimates are reasonably good for all surveys except the period 2015-2019 (Fig. 1.31). There are large positive residuals for the Shelikof Strait acoustic survey in 2017, 2018 and 2019, and strong negative residuals for the NMFS bottom trawl survey for 2017 and 2019. In addition, the model is unable to fit the extremely low values for the ADF&G survey in 2015-2017. The fit to the summer acoustic survey is reasonable even during the most recent period. The model shows good fits to both the 2021 Shelikof Strait acoustic survey and the 2021 NMFS bottom trawl, while the 2021 ADF&G bottom trawl and 2021 summer acoustic survey fits were reasonable. The fit to the age-1 and age-2 Shelikof acoustic indices was considered acceptable (Fig. 1.32).

Time series results

Parameter estimates and model output are presented in a series of tables and figures. Estimated survey and fishery selectivity for different periods are given in Table 1.19 (see also Fig. 1.33). Table 1.20 gives the estimated population numbers at age for the years 1970-2021. Table 1.21 gives the estimated time series of age 3+ population biomass, age-1 recruitment, and harvest rate (catch/3+ biomass) for 1977-2021 (see also Fig. 1.34). Table 1.22 gives coefficients of variation and 95% confidence intervals for age-1 recruitment and spawning stock biomass. Stock size peaked in the early 1980s at approximately 120% of the proxy for unfished stock size (B100% = mean 1978-2020 recruitment multiplied by the spawning biomass per recruit in the absence of fishing (SPR@F=0, see below for how this is calculated). In 2002, the stock dropped below the B40% for the first time since the early 1980s, and reached a minimum in 2003 of 35% of unfished stock size. Over the years 2009-2013 stock size showed a strong upward trend, increasing from 43% to 78% of unfished stock size, but declined to 54% of unfished stock size in 2015. The spawning stock peaked in 2017 at 83% as the strong 2012 year class matured, and has declined subsequently to 46% in 2021. Figure 1.35 shows the historical pattern of exploitation of the stock both as a time series of SPR and fishing mortality compared to the current estimates of biomass and fishing mortality reference points. Except from the mid-1970s to mid-1980s fishing mortalities have generally been lower than the current OFL definition, and in nearly all years were lower than the FMSY proxy of F35% .

Comparison of historical assessment results

A comparison of assessment results for the years 1993-2021 indicates the current estimated trend in spawning biomass for 1990-2021 is consistent with previous estimates (Fig. 1.36). All time series show a similar pattern of decreasing spawning biomass in the 1990s, a period of greater stability in 2000s, followed by an increase starting in 2008. The estimated 2021 age composition from the current assessment were very similar to the projected 2021 age composition from the 2020 assessment (Fig. 1.37). Generally, the two models agree except for the age 1 recruits, where the 2020 model assumed average recruitment, but the 2021 has data from the Shelikof survey which showed a strong year class. This difference does not strongly affect the OFL and ABC for next year because these fish are not in the exploitable population.

Retrospective analysis of base model

A retrospective analysis consists of dropping the data year-by-year from the current model, and provides an evaluation of the stability of the current model as new data are added. Figure 1.38 shows a retrospective plot with data sequentially removed back to 2011. There is up to 37% error in the estimates of spawning biomass (if the current assessment is accepted as truth), but usually the errors are much smaller (median absolute error is 11%). There is relatively minor positive retrospective pattern to errors in the assessment, and the revised Mohn’s \(\rho\) (Mohn 1999) across all ten peels for ending year spawning biomass is 0.056, which does not indicate a concern with retrospective bias.

Stock productivity

Recruitment of GOA pollock is more variable (CV = 1.27 over 1978-2020) than Eastern Bering Sea pollock (CV = 0.60). Other North Pacific groundfish stocks, such as sablefish and Pacific ocean perch, also have high recruitment variability. However, unlike sablefish and Pacific ocean perch, pollock have a short generation time (~8 years), so that large year classes do not persist in the population long enough to have a buffering effect on population variability. Because of these intrinsic population characteristics, the typical pattern of biomass variability for GOA pollock will be sharp increases due to strong recruitment, followed by periods of gradual decline until the next strong year class recruits to the population. GOA pollock is more likely to show this pattern than other groundfish stocks in the North Pacific due to the combination of a short generation time and high recruitment variability.

Since 1980, strong year classes have occurred periodically every four to six years (Fig. 1.34). Because of high recruitment variability, the mean relationship between spawning biomass and recruitment is difficult to estimate despite good contrast in spawning biomass. Strong and weak year classes have been produced at high and low level of spawning biomass. Spawner productivity is higher on average at low spawning biomass compared to high spawning biomass, indicating that survival of eggs to recruitment is density-dependent (Fig. 1.39). However, this pattern of density-dependent survival only emerges on a decadal scale, and could be confounded with environmental variability on the same temporal scale. The decadal trends in spawner productivity have produced the pattern of increase and decline in the GOA pollock population. The last two decades have been a period of relatively low spawner productivity, though there appears to be a recent increase. Age-1 recruitment in 2020 is estimated to be to be very weak, but the 2021 recruitment is above average, although these estimates will remain very uncertain until additional data become available.

Ecosystem Considerations

Ecosystem Effects on the Stock

1. Predator population trends (historically, in the present, and in the foreseeable future). These trends could affect stock mortality rates over time.
2. Changes in habitat quality (historically, in the present, and in the foreseeable future). Changes in the physical environment such as temperature, currents, or ice distribution could affect stock migration and distribution patterns, recruitment success, or direct effects of temperature on growth.

Fishery Effects on the Ecosystem

1. Fishery-specific contribution to bycatch of prohibited species, forage (including herring and juvenile pollock), HAPC biota (in particular, species common to the target fishery), marine mammals, birds, and other sensitive non-target species (including top predators such as sharks, expressed as a percentage of the total bycatch of that species.
2. Fishery-specific concentration of target catch in space and time relative to predator needs in space and time (if known) and relative to spawning components.
3. Fishery-specific effects on amount of large-size target fish.
4. Fishery-specific contribution to discards and offal production.
5. Fishery-specific effects on age at maturity and fecundity of the target species.
6. Fishery-specific effects on EFH non-living substrate (using gear specific fishing effort as a proxy for amount of possible substrate disturbance).

Data Gaps and Research Priorities

The following research priorities were identified based on previous CIE reviews and recent Plan Team and SSC discussions: • Explore alternative functional forms for fishery selectivity. • Jointly estimate process errors for time-varying components like selectivity, catchability and recruitment, using integration via the Laplace approximation or MCMC. • Consider alternative modeling platforms in parallel to the current ADMB assessment. • Explore priors on catchability and the effect on the population scale and potentially how it relates to results from the predation mortality model. • Revisit initial data weights for compositional data, and assumed CVs for indices. • Estimate input variances for weight at age components in the WAA RE model. • Continue to develop spatial GLMM models for survey indices and age composition of GOA pollock • Evaluate pollock population dynamics in a multi-species context using the CEATTLE model. • Explore implications of non-constant natural mortality on pollock assessment and management.

Additional recommendations that could be done by other teams at the AFSC, but are unlikely to be specifically prioritized by the primary assessment author, include: • Efforts to combine acoustic and bottom trawl information in a vertically integrated index • Efforts to improve understanding of changes of weight at age or and maturity at age, either via linkage to copepods/euphausiids or directly to the physical environment

A full ESP was developed for GOA pollock in 2020 and reviewed by the Plan Team at its September and November 2019 meetings. The GOA Groundfish Plan Team encouraged the authors to consider potential avenues for updating ESPs rather than producing full ESPs in the future. This year we provide a partial ESP in Appendix 1A that updates key indicators and reruns the Bayesian adaptive sampling model. We are soliciting feedback from the Plan Team and the SSC on the appropriate format and information to be included in an ESP update.

Acknowledgements

We thank the AFSC survey personnel for the collection of data and providing the biomass estimates, and Wayne Palsson for providing summarized data. We are grateful to all the fishery observers working with the Fishery Monitoring and Analysis (FMA) Division who collect vital data for the stock assessments, and the staff of the AFSC Age and Growth Unit for the ageing of otoliths used to determine the age compositions in the assessment. We also thank Kally Spalinger for providing ADF&G survey data.

References

Bailey, K.M., Stabeno, P.J. and Powers, D.A. (1997) The role of larval retention and transport features in mortality and potential gene flow of walleye pollock. J. Fish. Biol 51, 135–154.

Megrey, B.A. (1989) Exploitation of walleye pollock resources in the gulf of alaska, 1964-1988: Portrait of a fishery in transition. In: Proc. International symp. On the biology and management of walleye pollock, lowell wakefield fisheries symp., Alaska sea grant rep, Vol. 89-1. pp 33–58.

Mulligan, T.J., Chapman, R.W. and Brown, B.L. (1992) Mitochondrial DNA analysis of walleye pollock, theragra chalcogramma, from the eastern bering sea and shelikof strait, gulf of alaska. Can. J. Fish. Aquat. Sci 49, 319–326.

Trijoulet, V., Albertsen, C.M., Kristensen, K., Legault, C.M., Miller, T.J. and Nielsen, A. (2023) Model validation for compositional data in stock assessment models: Calculating residuals with correct properties. Fisheries Research 257, 106487.

Figures

Figure 1.1. Distribution of pollock catch in the 2020 fishery shown for 1/2 degree latitude by 1 degree longitude blocks by season in the Gulf of Alaska as determined by fishery observer-recorded haul retrieval locations. Blocks with less than 1.0 t of pollock catch are not shown. The area of the circle is proportional to the catch.

Figure 1.2. Distribution of pollock catch in the 2020 fishery shown for 1/2 degree latitude by 1 degree longitude blocks by season in the Gulf of Alaska as determined by fishery observer-recorded haul retrieval locations. Blocks with less than 1.0 t of pollock catch are not shown. The area of the circle is proportional to the catch.

{r ages-fsh, eval=TRUE, fig.cap=paste("GOA pollock fishery age composition (1975-",year-1,"). The area of the circle is proportional to the catch. Diagonal lines show strong year classes")}. addfig("ages_fsh".png')

Figure 1.3. Pollock catch per unit effort (CPUE) for the 2021 NMFS bottom trawl survey in the Gulf of Alaska (heights of purple bars). Red stars indicate hauls with no pollock catch.

Figure 1.4. Estimated abundance at age in the NMFS bottom trawl survey (1984-2021). The area of the circle is proportional to the estimated abundance.

Figure 1.5. Age composition of pollock by statistical area for the2021 NMFS bottom trawl survey.

Figure 1.6. Biomass trends from winter acoustic surveys of pre-spawning aggregations of pollock in the GOA.

Figure 1.7. Estimated abundance at age in the Shelikof Strait acoustic survey (1981-2022 except 1982, 1987, 1999, and 2011). The area of the circle is proportional to the estimated abundance.

Figure 1.8. Tow locations for the 2022 ADF&G crab/groundfish trawl survey.

Figure 1.9. Comparison of ADF&G crab/groundfish trawl area-swept indices with year indices for a delta GLM model with a gamma error assumption for the positive observations. Both time series have been scaled by the mean for the time series.

Figure 1.10. Estimated proportions at age in the ADF&G crab/groundfish survey (2000-2020). The area of the circle is proportional to the estimated abundance.

Figure 1.11. Relative trends in pollock biomass since 1990 for the Shelikof Strait acoustic survey, the NMFS bottom trawl survey, and the ADF&G crab/groundfish trawl survey. Each survey biomass estimate is standardized to the average since 1990. Shelikof Strait acoustic surveys prior to 2008 were re-scaled to be comparable to the surveys conducted from 2008 onwards by the R/V Oscar Dyson.

Figure 1.12. GOA pollock fishery catch characteristics.

Figure 1.13. Comparison of 2012 year class maturation, growth, and mortality with average characteristics. Maturity is based on sampling during winter acoustic surveys. Weight at age is a comparison of the 2012 year class in the winter acoustic survey with the average weight at age since 2013 excluding the 2012 year class. The mortality plot is catch curve analysis of the Shelikof Strait survey. The negative of the slope of a linear regression of log(N) on age is an estimate of total mortality (Z).

Figure 1.14. Prior on bottom trawl catchability used in the base model, and the estimate and uncertainty from the base model.

Figure 1.15. Alternative estimates of age-specific natural mortality. The scaled average was used in the stock assessment model.

Figure 1.16. Estimates of the proportion mature at age from weighted visual maturity data collected during2018-2022 winter acoustic surveys in the Gulf of Alaska and long-term average proportion mature at age (1983-2022). Maturity for age-1 fish is assumed to be zero.

Figure 1.17. Age at 50% mature (top) and length at 50% mature (bottom) from annual logistic regressions for female pollock from winter acoustic survey data in the Gulf of Alaska. Estimates since 2003 are weighted by local abundance.

Figure 1.18. Estimated weight at age of GOA pollock (ages 2, 4, 6, 8, and 10) from Shelikof Strait acoustic surveys used in the assessment model. In 1999 and 2011, when the acoustic survey was not conducted, weights-at-age were interpolated from surveys in adjacent years.

Figure 1.19. Comparison of fishery weight at age for 2021 with estimates from the random effects model last year and this year’ assessment (top panel). Random effects model estimates for 2022 used in the assessment model and for yield projections (bottom panel).

Figure 1.20. Changes in estimated spawning biomass as new data were added successively to last year’s base model, ordered by row in the legend at the top. The lower panel shows recent years with an expanded scale to highlight differences.

Figure 1.21. Time-varying catchability for the Shelikof Strait acoustic survey and the ADF&G crab/groundfish trawl survey for model 19.1 (2021).

Figure 1.22. Observed and predicted fishery age composition for GOA pollock from the base model. Dashed blue lines are observations and solid red lines are model expectations.

(#fig:pearson_fsh)Pearson residuals for fishery age composition. Negative residuals are filled blue and positive filled red. Circle area is proportional to the magnitude of the residual.

Figure 1.23. Observed and predicted Shelikof Strait acoustic survey age composition for GOA pollock from the base model. Dashed blue lines are observations and solid red lines are model expectations. Age 1 and 2 fish are modeled separately and excluded.

Figure 1.24. Pearson residuals for Shelikof Strait acoustic survey age composition. Negative residuals are filled blue and positive filled red. Circle area is proportional to the magnitude of the residual.

Figure 1.25. Observed and predicted NMFS bottom trawl age composition for GOA pollock from the base model (top). Dashed blue lines are observations and solid red lines are model expectations. Pearson residuals for NMFS bottom trawl survey (bottom). Negative residuals are filled blue and positive filled red. Circle area is proportional to the magnitude of the residual.

Figure 1.26. Observed and predicted ADF&G bottom trawl age composition for GOA pollock from the base model (top). Dashed blue lines are observations and solid red lines are model expectations. Pearson residuals for ADF&G bottom trawl survey (bottom). Negative residuals are filled blue and positive filled red. Circle area is proportional to the magnitude of the residual.

Figure 1.27. Model predicted (line) and observed survey biomass (points and 95% confidence intervals) for the four surveys. The Shelikof survey is only for ages 3+.

Figure 1.28. Model predicted (line) and observed survey biomass (points and 95% confidence intervals) for the age 1 and age 2 winter Shelikof surveys.

Figure 1.29. Estimates of time-varying double-logistic fishery selectivity for GOA pollock for the base model. The selectivity is scaled so the maximum in each year is 1.0.

Figure 1.30. Estimated time series of GOA pollock spawning biomass (top) and age 1 recruitment (bottom) for the base model, with horizontal line at the average from 1978-2021. Vertical bars represent two standard deviations. The B35% and B40% lines represent the current estimate of these benchmarks.

Figure 1.31. Annual fishing mortality as measured in percentage of unfished spawning biomass per recruit (top). GOA pollock spawning biomass relative to the unfished level and fishing mortality relative to FMSY (bottom). The ratio of fishing mortality to FMSY is calculated using the estimated selectivity pattern in that year. Estimates of B100% spawning biomass are based on current estimates of maturity at age, weight at age, and mean recruitment. Because these estimates change as new data become available, this figure can only be used in a general way to evaluate management performance relative to biomass and fishing mortality reference levels.

Figure 1.32. Estimated female spawning biomass for historical stock assessments conducted between 2000-2021. Lines reprsent the estimate in the assessment year and point is the terminal estimate in that year.

Figure 1.33. The bottom panel shows the estimated age composition in 2022 from the 2021 and 2022 assessments.

{r retros, eval=TRUE, fig.cap=paste0("Retrospective plot of spawning biomass for models ending in years ",year-9,"-",year-1, " for the ",year," base model. The revised Mohn’s rho (Mohn 1999) for ending year spawning biomass is -0.051.")} <--todo fix this as code--> addfig("retros.png")

Figure 1.34. GOA pollock spawner productivity, log(R/S), in 1970-2019 (top). A five-year running average is also shown. Spawner productivity in relation to female spawning biomass (bottom). The Ricker stock-recruit curve is linear in a plot of spawner productivity against spawning biomass.

Figure 1.35. Uncertainty in spawning biomass in 2022-2026 based on a posterior samples from MCMC from the joint likelihood for the base model where catch is set to the maximum permissible FABC. Shown are the percentage below the horizontal line at 20% for each year.

Figure 1.36. Projected mean spawning biomass and catches in 2020-2025 under different harvest rates.